Schumer on Monday called on the U.S. government to expand its Secure Flight Program, which cross-checks air travelers against a security watch list, to keep anyone on the no-fly list off trains. Basically, a train passenger would have to present ID, and his or her name would be checked against a list of suspected terrorists, FoxNews.com reported. If there were a match, that individual wouldn't be allowed to board the train.

In a statement Monday, John O'Connor, Amtrak's vice president and chief of police, did not rule out a "no-ride" list, but he also alluded to potential issues.

"Amtrak is committed to the safety and security of our passengers and remains a safe way to travel," O'Connor said. "All countermeasures add value in creating an overall security posture in protecting a rail system that operates in an open environment. The creation of a 'do not ride' list is no exception.

"It would, however, have to be developed in close coordination with the Transportation Security Administration (TSA) and implemented in a way that respects civil rights and allows for the rapid flow of persons and trains, necessary for effective mass transit."

The Department of Homeland Security did not issue a position on the idea of a no-ride list, saying instead that Secretary Janet Napolitano would respond to Schumer directly. But a spokesman did outline its efforts to safeguard rail travel.

Spokesman Adam Fetcher said that, since 2006, the department had awarded $1.6 billion in grants to the transit and passenger rail industry to boost security.

Fetcher also said the department had funding in its 2012 budget to add a dozen more "multi-modal Visual Intermodal Prevention & Response teams" or VIPRs (pronounced "vipers"), bringing the total number of teams to 37. These teams are described as air marshals, K-9 units or security inspectors who unpredictably swarm ferries, trains and airports as a deterrent to terrorists.

Do you think a "no-ride" list is a good or bad idea? Vote in this poll, or add to the "Comments" section below.